The problem states that there are 5 male students and 8 female students who have good poetry writing skills. The teacher wants to select 3 male students and 4 female students to present their work in a certain order. We need to find out how many ways the teacher can select these students.

1. Problem Description

The problem states that there are 5 male students and 8 female students who have good poetry writing skills. The teacher wants to select 3 male students and 4 female students to present their work in a certain order. We need to find out how many ways the teacher can select these students.

2. Solution Steps

First, we need to calculate the number of ways to choose 3 male students from 5, which is a combination problem. The formula for combinations is:

$C(n, k) = \frac{n!}{k!(n-k)!}$

where $n$ is the total number of items, $k$ is the number of items to choose, and $!$ denotes the factorial.

The number of ways to choose 3 male students from 5 is:

$C(5, 3) = \frac{5!}{3!(5-3)!} = \frac{5!}{3!2!} = \frac{5 \times 4 \times 3 \times 2 \times 1}{(3 \times 2 \times 1)(2 \times 1)} = \frac{5 \times 4}{2} = 10$

Next, we need to calculate the number of ways to choose 4 female students from 8:

$C(8, 4) = \frac{8!}{4!(8-4)!} = \frac{8!}{4!4!} = \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(4 \times 3 \times 2 \times 1)(4 \times 3 \times 2 \times 1)} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} = \frac{8 \times 7 \times 6 \times 5}{24} = 70$

Now, we have 10 ways to choose the male students and 70 ways to choose the female students. Since these choices are independent, we multiply the number of ways to choose the males and females.

$10 \times 70 = 700$

After choosing the students, we need to arrange them in a certain order. We have 3 male students and 4 female students, making a total of 7 students. The number of ways to arrange 7 students is $7!$.

$7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040$

Finally, we multiply the number of ways to choose the students ($700$) by the number of ways to arrange them ($5040$).

$700 \times 5040 = 3528000$

3. Final Answer

The teacher can select and arrange the students in 3,528,000 ways.